Bifurcation analysis of ion-acoustic waves in an adiabatic trapped electron and warm ion plasma

Abstract

Bifurcation analysis of ion-acoustic waves in complex plasmas in the presence of adiabatic trapped electrons and warm ions is studied. Using bifurcation theory of dynamical structure, the Hamiltonian system inculpated electrostatic potential is derived. Effects of physical parameters, such as T and σ i , are shown on the analytical solitary wave solution. The numerical results show that parameters T and σ i affect significantly on nonlinear electrostatic solitary waves. By adding an external periodic perturbation to unperturbed Hamiltonian system, we investigate quasiperiodic structure of the perturbed Hamiltonian system.

Stability of dust-acoustic solitary waves in magnetized dusty plasmas: effect of polarization force and degenerate electron temperature

“…Thus, the normalized temperature degenerate trapped electrons number density [21][22][23][24][25][26] reads…”

“…It was seen that adiabatic trapping produced 3/2 power nonlinearity instead of the usual quadratic one without trapping. In trapping, some plasma particles are confined in a finite region of space region, bounce back and forth, and show the closed trajectories [21]. The particles trapping in quantum plasma can be introduced via the Gurevich approach [20] and Shah et al [22] has used this approach to model one-dimensional ion acoustic solitary structures in both partially and fully degenerate quantum plasma with small temperature effects.…”

Qualitative analysis and new soliton solutions for the coupled nonlinear Schrödinger type equations

“…In this section, we are interested in studying the autoresonance phenomenon for the non-autonomous oscillatory system. The core of the phenomenon is that the oscillator self-adjusts with varying external periodic force so that the oscillator stays in resonance for a long time which implies varying in the response amplitude under weak driving perturbation [36,37]. The perturbed form of dynamical system (1.1) after inserting the periodic term w and q are named the strength and frequency of the external periodic perturbation.…”

“…The bifurcation theory analysis is one of the most common methods in dealing with a system of differential equations; see e.g. [28][29][30][31][32][33][34][35][36][37][38][39]. Recent methods dealing with NLEEs are generalized exponential rational function method [40], ameliorated form of a modified F-expansion method [41], Φ 6 − model expansion method [42] and the super thermal index method [43].…”

“…Recently, a great interest in studying the evaluation equations including periodic perturbation term, see, e.g. [36,37,[51][52][53][54][55][56]. Although there are several periodic perturbations in distinct physical problems, the nature of these periodic perturbed terms differs relying on the physics of the problems.…”